arXiv subjects

Fariel Shafee

Publications and source records attributed to Fariel Shafee.

31 records · Page 2Linked to original sources

arXiv2004

Optimal Control of Quantum Systems and a Generalized Level Set Method

We study the application of a generalized form of the level set method used in classical physical contexts to quantum optimal control situations. The set of OCT equations needed to keep the expectation value of an observable constant is first discussed and the dimensionality of the actual parameter space carefully considered. Then we see how concepts of level set methods emerge that may help solve the inverse problem associated with designing the control Hamiltonian with greater speed. The formal equations and the algorithm are presented.

quant-ph↗

arXiv2004

Quantum Control with Level Set Method

We examine the relevance of Level Set Methods (LSM)in coherent control quantum systems where the objective is to retain or attain a particular expectation value of a given measurable. The differences with the usual applications of LSM, where continuous closed interfaces are involved, and the quantum case, where we may have a discrete number of points to deal with, are noted. The question of optimization in this new context is also clarified. Simple examples with symmetric and asymmetric multidimensional potentials are briefly considered.

quant-ph↗

arXiv2004

Evolution of Level Sets in Hamilton Parameter Space

We develop a formalism to study the use of Level Set Method (LSM) in the investigation of evolution of observables in terms of parameters of the Hamiltonian, both of the system itself and the control part. A simple example with an analytic solution available perturbatively is examined. We show that B splines can quite accurately and smoothly interpolate surfaces corresponding to constant expectation value of observables which form the level sets as projections on a finite mesh of data. Lastly we make a brief priliminary scrutiny of teh possibility of using temperature as a relevant parameter in ensembles of quantum systems.

quant-ph↗

arXiv2004

Chaos and Annealing in Social networks

In this work we compare social clusters with spin clusters and compare different properties. We also try to compare phase changes in market and labor stratification with phase changes of spin clusters. Then we compare the requisites for redrawing the boundaries of social clusters with respect to energy minimization and efficiency. We finally do a simulation experiment and show that by choosing suitable link matrices for agents and attributes of the same and of different agents it is possible to have at the same time behavior similar to chaos or punctuated equilibrium in some attributes or fairly regular oscillations of preferences for other attributes, using greatest utility or efficiency as a criterion for change in conflicting social networks with different agents having different preferences with respect to the attributes in the agent himself or with similar attributes in other agents.

cond-mat.dis-nn↗

arXiv2004

Generalized Entropies and Statistical Mechanics

We consider the problem of defining free energy and other thermodynamic functions when the entropy is given as a general function of the probablity distribution, including that for non extensive forms. We find that the free energy, which is central to the determination of all other quantities, can be obtained uniquely numerically ebven when it is the root of a transcendental equation. In particular we study the cases for Tsallis form and a new form proposed by us recently. We compare the free energy, the internal energy and the specific heat of a simple system two energy states for each of these forms.

cond-mat.stat-mech↗

arXiv2004

Entangled Quantum Networks

We present some results from simulation of a network of nodes connected by c-NOT gates with nearest neighbors. Though initially we begin with pure states of varying boundary conditions, the updating with time quickly involves a complicated entanglement involving all or most nodes. As a normal c-NOT gate, though unitary for a single pair of nodes, seems to be not so when used in a network in a naive way, we use a manifestly unitary form of the transition matrix with c?-NOT gates, which invert the phase as well as flipping the qubit. This leads to complete entanglement of the net, but with variable coefficients for the different components of the superposition. It is interesting to note that by a simple logical back projection the original input state can be recovered in most cases. We also prove that it is not possible for a sequence of unitary operators working on a net to make it move from an aperiodic regime to a periodic one, unlike some classical cases where phase-locking happens in course of evolution. However, we show that it is possible to introduce by hand periodic orbits to sets of initial states, which may be useful in forming dynamic pattern recognition systems.

quant-ph↗

arXiv2004

Semiclassical Neural Network

We have constructed a simple semiclassical model of neural network where neurons have quantum links with one another in a chosen way and affect one another in a fashion analogous to action potentials. We have examined the role of stochasticity introduced by the quantum potential and compare the system with the classical system of an integrate-and-fire model by Hopfield. Average periodicity and short term retentivity of input memory are noted.

quant-ph↗

arXiv2004

Neural Networks with c-NOT Gated Nodes

We try to design a quantum neural network with qubits instead of classical neurons with deterministic states, and also with quantum operators replacing teh classical action potentials. With our choice of gates interconnecting teh neural lattice, it appears that the state of the system behaves in ways reflecting both the strengths of coupling between neurons as well as initial conditions. We find that depending whether there is a threshold for emission from excited to ground state, the system shows either aperiodic oscillations or coherent ones with periodicity depending on the strength of coupling.

quant-ph↗

arXiv2004

A New Nonextensive Entropy

We propose a new way of defining entropy of a system, which gives a general form which may be nonextensive as Tsallis entropy, but is linearly dependent on component entropies, like Renyi entropy, which is extensive. This entropy has a conceptually novel but simple origin and is mathematically easy to define by a very simple expression, though the probability distribution resulting from optimizing it gives rather complex, which is compared numerically with the other entropies. It may, therefore, appear as the right candidate in a physical situation where the probability distribution does not suit any of the previously defined forms.

nlin.AO↗

arXiv2003

Quantum Control of Expectation Values of Observables

We study the changes if any of the expectation value of a general observable in a quantum system, the difficulties associated with the detection of these changes, and the possible methods for correcting the system through unitary control to maintain a constant average expectation value of the observable.

quant-ph↗

arXiv2003

Space-Filling Curves for Quantum Control Parameters

We consider the use of space-filling curves (SFC) in scanning control parameters for quantum chemical systems. First we show that a formally exact SFC must be singular in the control parameters, but a finite discrete generalization can be used with no problem. We then make general observations about the relevance of SFCs in preference to linear scans of the parameters. Finally we present a simple magnetic field example relevant in NMR and show from the calculated autocorrelations that a SFC Peano-Hilbert curve gives a smoother sequence than a linear scan.

quant-ph↗

arXiv2002

A Spin Glass Model of Human Logic Systems

In this paper, we discuss different models for human logic systems and describe a game with nature. Gödel`s incompleteness theorem is taken into account to construct a model of logical networks based on axioms obtained by symmetry breaking. These classical logic networks are then coupled using rules that depend on whether two networks contain axioms or anti-axioms. The social lattice of axiom based logic networks is then placed with the environment network in a game including entropy as a cost factor. The classical logical networks are then replaced with ``preference axioms'' to the role of fuzzy logic.

nlin.AO↗

arXiv2002

Entropy and inference, revisited

We study properties of popular near-uniform (Dirichlet) priors for learning undersampled probability distributions on discrete nonmetric spaces and show that they lead to disastrous results. However, an Occam-style phase space argument expands the priors into their infinite mixture and resolves most of the observed problems. This leads to a surprisingly good estimator of entropies of discrete distributions.

physics.data-an↗